Question

A small block slides along a path which is smooth until the block reaches the section of length L = 3m, which begins at height h = 3m on a flat incline of angle ${37}^{\circ }$, as shown in the figure. In that section, the coefficient of kinetic friction is 0.50. The block passes through point A with a speed of $\sqrt{136}$ m/s. Find the speed (in m/s) of the block as it passes through point B where the friction ends. ($g=10m/s^2$)

___

Answer 1

$\frac{1}{2}m{v}^2=\frac{1}{2}m(\sqrt{136}{)}^2-\left[mg\right(3)+mg\frac{9}{5}+\mu mg\frac{12}{5}]\Rightarrow v^2=136-2[30+18+12]=16\Rightarrow v=4m/s$